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Research Papers: Design of Mechanisms and Robotic Systems

A Versatile 3R Pseudo-Rigid-Body Model for Initially Curved and Straight Compliant Beams of Uniform Cross section

[+] Author and Article Information
Venkatasubramanian Kalpathy Venkiteswaran

Department of Biomechanical Engineering,
University of Twente,
Drienerlolaan 5,
Enschede 7522 NB, The Netherlands
e-mail: v.kalpathyvenkiteswaran@utwente.nl

Hai-Jun Su

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: su.298@osu.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 8, 2018; final manuscript received June 9, 2018; published online July 9, 2018. Assoc. Editor: Dar-Zen Chen.

J. Mech. Des 140(9), 092305 (Jul 09, 2018) (8 pages) Paper No: MD-18-1111; doi: 10.1115/1.4040628 History: Received February 08, 2018; Revised June 09, 2018

Rigid-body discretization of continuum elements was developed as a method for simplifying the kinematics of otherwise complex systems. Recent work on pseudo-rigid-body (PRB) models for compliant mechanisms has opened up the possibility of using similar concepts for synthesis and design, while incorporating various types of flexible elements within the same framework. In this paper, an idea for combining initially curved and straight beams within planar compliant mechanisms is developed to create a set of equations that can be used to analyze various designs and topologies. A PRB model with three revolute joints is derived to approximate the behavior of initially curved compliant beams, while treating straight beams as a special case (zero curvature). The optimized model parameter values are tabled for a range of arc angles. The general kinematic and static equations for a single-loop mechanism are shown, with an example to illustrate accuracy for shape and displacement . Finally, this framework is used for the design of a compliant constant force mechanism to illustrate its application, and comparisons with finite element analysis (FEA) are provided for validation.

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Figures

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Fig. 1

A straight beam can act as a line constraint between two points (assuming no buckling), whereas a curved beam has behavior similar to a stiff prismatic joint

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Fig. 2

Initially curved beam subject to tip loads

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Fig. 3

Symmetric 3R PRB model for initially curved beams before and after deformation

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Fig. 4

Plots showing the variation of the optimal PRB parameters as a function of the arc angle, ψ in radians. The result at ψ = 0 represents a straight beam. The optimization was performed at 15 deg intervals. The curves are polynomial fitting functions presented at the end of Sec. 2.3.

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Fig. 5

Schematic of a single-loop compliant mechanism with multiple beams subjected to a load of force F and moment M (above) and one beam shown separately for defining variables (below)

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Fig. 6

Shape of a three beam compliant mechanism with two curved and one straight beam calculated using FEA and the PRB model described in this paper

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Fig. 7

Comparison of displacement of P2 from Fig. 6 under the action of load F

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Fig. 8

Schematic of one half of a symmetric compliant mechanism. Each half has three beams, which may be curved or straight. The thick black dotted lines represent one possible topology with two curved beams and one straight beam.

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Fig. 9

The optimized version of the constant-force mechanism analyzed using FEA. The undeformed mechanism is shown in white, and the stress variation is illustrated in the deformed mechanism.

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Fig. 10

Comparison of results from FEA and PRB analysis. The plot at the top shows the change in strain energy versus the displacement and the one at the bottom is the plot for force.

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